1. Quant Reading 6 Hypothesis Testing Answers

Question #1 of 86

Question ID: 1456649

An analyst is testing the hypothesis that the mean excess return from a trading strategy is
less than or equal to zero. The analyst reports that this hypothesis test produces a p-value of
0.034. This result most likely suggests that the:

A) best estimate of the mean excess return produced by the strategy is 3.4%.
B) null hypothesis can be rejected at the 5% significance level.
C) smallest significance level at which the null hypothesis can be rejected is 6.8%.
Explanation
A p-value of 0.035 means the hypothesis can be rejected at a significance level of 3.5% or
higher. Thus, the hypothesis can be rejected at the 10% or 5% significance level, but
cannot be rejected at the 1% significance level.

(Module 6.2, LOS 6.e)

Question #2 of 86

Question ID: 1456618

Which of the following statements about hypothesis testing is most accurate?

A)
B)
C)

A Type I error is rejecting the null hypothesis when it is true, and a Type II error
is rejecting the alternative hypothesis when it is true.
A hypothesis that the population mean is less than or equal to 5 should be

rejected when the critical Z-statistic is greater than the sample Z-statistic.
A hypothesized mean of 3, a sample mean of 6, and a standard error of the
sampling means of 2 give a sample Z-statistic of 1.5.

Explanation
Z = (6 - 3)/2 = 1.5. A Type II error is failing to reject the null hypothesis when it is false. The
null hypothesis that the population mean is less than or equal to 5 should be rejected
when the sample Z-statistic is greater than the critical Z-statistic.

(Module 6.1, LOS 6.c)


Question #3 of 86

Question ID: 1456607

Which of the following is an accurate formulation of null and alternative hypotheses?

A) Less than for the null and greater than for the alternative.
B) Equal to for the null and not equal to for the alternative.
C) Greater than for the null and less than or equal to for the alternative.
Explanation
A correctly formulated set of hypotheses will have the "equal to" condition in the null
hypothesis.
(Module 6.1, LOS 6.a)

Question #4 of 86

Question ID: 1456642

An analyst calculates that the mean of a sample of 200 observations is 5. The analyst wants
to determine whether the calculated mean, which has a standard error of the sample
statistic of 1, is significantly different from 7 at the 5% level of significance. Which of the
following statements is least accurate?:

A) The alternative hypothesis would be Ha: mean > 7.
B) The null hypothesis would be: H0: mean = 7.
C)

The mean observation is significantly different from 7, because the calculated Zstatistic is less than the critical Z-statistic.

Explanation
The way the question is worded, this is a two tailed test. The alternative hypothesis is not
Ha: M > 7 because in a two-tailed test the alternative is =, while < and > indicate one-tailed
tests. A test statistic is calculated by subtracting the hypothesized parameter from the
parameter that has been estimated and dividing the difference by the standard error of
the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) /
(standard error of the sample statistic) = (5 - 7) / (1) = -2. The calculated Z is -2, while the
critical value is -1.96. The calculated test statistic of -2 falls to the left of the critical Zstatistic of -1.96, and is in the rejection region. Thus, the null hypothesis is rejected and
the conclusion is that the sample mean of 5 is significantly different than 7. What the
negative sign shows is that the mean is less than 7; a positive sign would indicate that the
mean is more than 7. The way the null hypothesis is written, it makes no difference
whether the mean is more or less than 7, just that it is not 7.
(Module 6.1, LOS 6.c)


Question #5 of 86

Question ID: 1456669

An analyst wants to determine whether the mean returns on two stocks over the last year
were the same or not. What test should she use, assuming returns are normally distributed?

A) Chi-square test.
B) Difference in means test.
C) Paired comparisons test.
Explanation
Portfolio theory teaches us that returns on two stocks over the same time period are
unlikely to be independent since both have some systematic risk. Because the samples are
not independent, a paired comparisons test is appropriate to test whether the means of
the two stocks' returns distributions are equal. A difference in means test is not
appropriate because it requires that the samples be independent. A chi-square test
compares the variance of a sample to a hypothesized variance.

(Module 6.3, LOS 6.i)

Question #6 of 86

Question ID: 1456622

A survey is taken to determine whether the average starting salaries of CFA charterholders is
equal to or greater than $57,000 per year. Assuming a normal distribution, what is the test
statistic given a sample of 115 newly acquired CFA charterholders with a mean starting
salary of $65,000 and a standard deviation of $4,500?

A) 19.06.
B) 1.78.
C) -19.06.
Explanation
With a large sample size (115) the z-statistic is used. The z-statistic is calculated by

subtracting the hypothesized parameter from the parameter that has been estimated and
dividing the difference by the standard error of the sample statistic. Here, the test statistic
= (sample mean – hypothesized mean) / (population standard deviation / (sample size)1/2 =
(X − µ) / (σ / n1/2) = (65,000 – 57,000) / (4,500 / 1151/2) = (8,000) / (4,500 / 10.72) = 19.06.
(Module 6.1, LOS 6.c)


Question #7 of 86

Question ID: 1456637

If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the
null is true, it is most likely that:

A) the confidence level of the test is 95%.
B) the power of the test is 95%.
C) the probability of a Type I error is 2.5%.
Explanation
Rejecting the null hypothesis when it is true is a Type I error. The probability of a Type I
error is the significance level of the test and one minus the significance level is the
confidence level. The power of a test is one minus the probability of a Type II error, which
cannot be calculated from the information given. (Module 6.1, LOS 6.c)

Question #8 of 86

Question ID: 1456670

Joe Sutton is evaluating the effects of the 1987 market decline on the volume of trading.
Specifically, he wants to test whether the decline affected trading volume. He selected a
sample of 500 companies and collected data on the total annual volume for one year prior

to the decline and for one year following the decline. What is the set of hypotheses that
Sutton is testing?

A) H0: µd = µd0 versus Ha: µd > µd0.
B) H0: µd = µd0 versus Ha: µd ≠ µd0.
C) H0: µd ≠ µd0 versus Ha: µd = µd0.
Explanation
This is a paired comparison because the sample cases are not independent (i.e., there is a
before and an after for each stock). Note that the test is two-tailed, t-test.

(Module 6.3, LOS 6.i)

Question #9 of 86

Question ID: 1456639


Kyra Mosby, M.D., has a patient who is complaining of severe abdominal pain. Based on an
examination and the results from laboratory tests, Mosby states the following diagnosis
hypothesis: Ho: Appendicitis, HA: Not Appendicitis. Dr. Mosby removes the patient's
appendix and the patient still complains of pain. Subsequent tests show that the gall bladder
was causing the problem. By taking out the patient's appendix, Dr. Mosby:

A) made a Type II error.
B) made a Type I error.
C) is correct.
Explanation
This statement is an example of a Type II error, which occurs when you fail to reject a
hypothesis when it is actually false.
The other statements are incorrect. A Type I error is the rejection of a hypothesis when it

is actually true.
(Module 6.1, LOS 6.c)

Question #10 of 86

Question ID: 1456624

A survey is taken to determine whether the average starting salaries of CFA charterholders is
equal to or greater than $58,500 per year. What is the test statistic given a sample of 175
CFA charterholders with a mean starting salary of $67,000 and a standard deviation of
$5,200?

A) 1.63.
B) –1.63.
C) 21.62.
Explanation
With a large sample size (175) the z-statistic is used. The z-statistic is calculated by
subtracting the hypothesized parameter from the parameter that has been estimated and
dividing the difference by the standard error of the sample statistic. Here, the test statistic
= (sample mean – hypothesized mean) / (population standard deviation / (sample size)1/2 =
(X − µ) / (σ / n1/2) = (67,000 – 58,500) / (5,200 / 1751/2) = (8,500) / (5,200 / 13.22) = 21.62.

(Module 6.1, LOS 6.c)


Question #11 of 86

Question ID: 1456677

The use of the F-distributed test statistic, F = s12 / s22, to compare the variances of two

populations least likely requires which of the following?

A) samples are independent of one another.
B) populations are normally distributed.
C) two samples are of the same size.
Explanation
The F-statistic can be computed using samples of different sizes. That is, n1 need not be
equal to n2.
(Module 6.4, LOS 6.j)

Question #12 of 86

Question ID: 1456602

Which one of the following best characterizes the alternative hypothesis? The alternative
hypothesis is usually the:

A) hypothesis that is accepted after a statistical test is conducted.
B) hypothesis to be proved through statistical testing.
C) hoped-for outcome.
Explanation
The alternative hypothesis is typically the hypothesis that a researcher hopes to support
after a statistical test is carried out. We can reject or fail to reject the null, not 'prove' a
hypothesis.
(Module 6.1, LOS 6.a)

Question #13 of 86
If the probability of a Type I error decreases, then the probability of:

A) a Type II error increases.

B) incorrectly accepting the null decreases.
C) incorrectly rejecting the null increases.

Question ID: 1456619


Explanation
If P(Type I error) decreases, then P(Type II error) increases. A null hypothesis is never
accepted. We can only fail to reject the null.
(Module 6.1, LOS 6.c)

Question #14 of 86

Question ID: 1456636

If a one-tailed z-test uses a 5% significance level, the test will reject a:

A) false null hypothesis 95% of the time.
B) true null hypothesis 95% of the time.
C) true null hypothesis 5% of the time.
Explanation
The level of significance is the probability of rejecting the null hypothesis when it is true.
The probability of rejecting the null when it is false is the power of a test. (Module 6.1, LOS
6.c)

Question #15 of 86

Question ID: 1456611

George Appleton believes that the average return on equity in the amusement industry, µ, is

greater than 10%. What is the null (H0) and alternative (Ha) hypothesis for his study?

A) H0: ≤ 0.10 versus Ha: > 0.10.
B) H0: > 0.10 versus Ha: < 0.10.
C) H0: > 0.10 versus Ha: ≤ 0.10.
Explanation
The alternative hypothesis is determined by the theory or the belief. The researcher
specifies the null as the hypothesis that he wishes to reject (in favor of the alternative).
Note that this is a one-sided alternative because of the "greater than" belief.
(Module 6.1, LOS 6.b)

Question #16 of 86

Question ID: 1456666


For a test of the equality of the means of two normally distributed independent populations,
the appropriate test statistic follows a:

A) chi-square distribution.
B) F-distribution.
C) t-distribution.
Explanation
The test statistic for the equality of the means of two normally distributed independent
populations is a t-statistic and equality is rejected if it lies outside the upper and lower
critical values.

(Module 6.3, LOS 6.h)

Question #17 of 86

Question ID: 1456617

A researcher is testing whether the average age of employees in a large firm is statistically
different from 35 years (either above or below). A sample is drawn of 250 employees and the
researcher determines that the appropriate critical value for the test statistic is 1.96. The
value of the computed test statistic is 4.35. Given this information, which of the following
statements is least accurate? The test:

A) has a significance level of 95%.
B) indicates that the researcher will reject the null hypothesis.
C)

indicates that the researcher is 95% confident that the average employee age is
different than 35 years.

Explanation
This test has a significance level of 5%. The relationship between confidence and
significance is: significance level = 1 – confidence level. We know that the significance level
is 5% because the sample size is large and the critical value of the test statistic is 1.96
(2.5% of probability is in both the upper and lower tails).
(Module 6.1, LOS 6.c)

Question #18 of 86

Question ID: 1456654

Which of the following statements about testing a hypothesis using a Z-test is least accurate?

The confidence interval for a two-tailed test of a population mean at the 5%
A) level of significance is that the sample mean falls between ±1.96 σ/√n of the null
hypothesis value.
B)

If the calculated Z-statistic lies outside the critical Z-statistic range, the null
hypothesis can be rejected.

C) The calculated Z-statistic determines the appropriate significance level to use.
Explanation
The significance level is chosen before the test so the calculated Z-statistic can be
compared to an appropriate critical value.
(Module 6.2, LOS 6.g)

Question #19 of 86

Question ID: 1456668

For a test of the equality of the mean returns of two non-independent populations based on
a sample, the numerator of the appropriate test statistic is the:

A) average difference between pairs of returns.
B) difference between the sample means for each population.
C) larger of the two sample means.
Explanation
A hypothesis test of the equality of the means of two normally distributed nonindependent populations (hypothesized mean difference = 0) is a t-test and the numerator
is the average difference between the sample returns over the sample period.

(Module 6.3, LOS 6.i)

Question #20 of 86

Question ID: 1456646

A researcher determines that the mean annual return over the last 10 years for an
investment strategy was greater than that of an index portfolio of equal risk with a statistical
significance level of 1%. To determine whether the abnormal portfolio returns to the
strategy are economically meaningful, it would be most appropriate to additionally account
for:


A) only the transaction costs and tax effects of the strategy.
B) only the transaction costs of the strategy.
C) the transaction costs, tax effects, and risk of the strategy.
Explanation
A statistically significant excess of mean strategy return over the return of an index or
benchmark portfolio may not be economically meaningful because of 1) the transaction
costs of implementing the strategy, 2) the increase in taxes incurred by using the strategy,
3) the risk of the strategy. Although the market risk of the strategy portfolios is matched to
that of the index portfolio, variability in the annual strategy returns introduces additional
risk that must be considered before we can determine whether the results of the analysis
are economically meaningful, that is, whether we should invest according to the strategy.
(Module 6.1, LOS 6.d)

Question #21 of 86

Question ID: 1456659

Student's t-Distribution
Level of Significance for One-Tailed Test

df 0.100 0.050 0.025 0.01 0.005 0.0005
Level of Significance for Two-Tailed Test
df

0.20

0.10

0.05

0.02

0.01

0.001

28 1.313 1.701 2.048 2.467 2.763

3.674

29 1.311 1.699 2.045 2.462 2.756

3.659

30 1.310 1.697 2.042 2.457 2.750

3.646

In order to test whether the mean IQ of employees in an organization is greater than 100, a
sample of 30 employees is taken and the sample value of the computed test statistic, tn-1 =

3.4. If you choose a 5% significance level you should:

A)
B)
C)

reject the null hypothesis and conclude that the population mean is greater
than 100.
fail to reject the null hypothesis and conclude that the population mean is
greater than 100.
fail to reject the null hypothesis and conclude that the population mean is less
than or equal to 100.


Explanation
At a 5% significance level, the critical t-statistic using the Student's t distribution table for a
one-tailed test and 29 degrees of freedom (sample size of 30 less 1) is 1.699 (with a large
sample size the critical z-statistic of 1.645 may be used). Because the calculated t-statistic
of 3.4 is greater than the critical t-statistic of 1.699, meaning that the calculated t-statistic
is in the rejection range, we reject the null hypothesis and we conclude that the
population mean is greater than 100.
(Module 6.2, LOS 6.g)

Question #22 of 86

Question ID: 1456604

Which of the following statements least accurately describes the procedure for testing a
hypothesis?

A) Develop a hypothesis, compute the test statistic, and make a decision.
B) Select the level of significance, formulate the decision rule, and make a decision.
C)

Compute the sample value of the test statistic, set up a rejection (critical) region,
and make a decision.

Explanation
Depending upon the author there can be as many as seven steps in hypothesis testing
which are:
1. Stating the hypotheses.
2. Identifying the test statistic and its probability distribution.
3. Specifying the significance level.
4. Stating the decision rule.
5. Collecting the data and performing the calculations.
6. Making the statistical decision.
7. Making the economic or investment decision.
(Module 6.1, LOS 6.a)

Question #23 of 86

Question ID: 1456667

Brandon Ratliff is investigating whether the mean of abnormal returns earned by portfolio
managers with an MBA degree significantly differs from mean abnormal returns earned by
managers without an MBA. Ratliff's null hypothesis is that the means are equal. If Ratliff's
critical t-value is 1.98 and his computed t-statistic is 2.05, he should:

A) reject the null hypothesis and conclude that the population means are equal.

B)
C)

reject the null hypothesis and conclude that the population means are not
equal.
fail to reject the null hypothesis and conclude that the population means are
equal.

Explanation
The hypothesis test is a two-tailed test of equality of the population means. The t-statistic
is greater than the critical t-value. Therefore, Ratliff can reject the null hypothesis that the
population means are equal.
(Module 6.3, LOS 6.h)

Question #24 of 86

Question ID: 1456656

Student's t-Distribution
Level of Significance for One-Tailed Test
df 0.100 0.050 0.025 0.01 0.005 0.0005
Level of Significance for Two-Tailed Test
df

0.20

0.10

0.05

0.02

0.01

0.001

40 1.303 1.684 2.021 2.423 2.704

3.551

Ken Wallace is interested in testing whether the average price to earnings (P/E) of firms in
the retail industry is 25. Using a t-distributed test statistic and a 5% level of significance, the
critical values for a sample of 41 firms is (are):

A) -1.685 and 1.685.
B) -1.96 and 1.96.
C) -2.021 and 2.021.
Explanation
There are 41 − 1 = 40 degrees of freedom and the test is two-tailed. Therefore, the critical
t-values are ± 2.021. The value 2.021 is the critical value for a one-tailed probability of
2.5%.
(Module 6.2, LOS 6.g)

Question #25 of 86


Question #25 of 86

Question ID: 1456629

A Type II error:

A) fails to reject a false null hypothesis.
B) fails to reject a true null hypothesis.
C) rejects a true null hypothesis.
Explanation
A Type II error is defined as accepting the null hypothesis when it is actually false. The
chance of making a Type II error is called beta risk.
(Module 6.1, LOS 6.c)

Question #26 of 86

Question ID: 1456655

Segment of the table of critical values for Student's t-distribution:
Level of Significance for a One-Tailed Test
df

0.050

0.025

Level of Significance for a Two-Tailed Test
df

0.10

0.05

18

1.734

2.101

19

1.729

2.093

Simone Mak is a television network advertising executive. One of her responsibilities is
selling commercial spots for a successful weekly sitcom. If the average share of viewers for
this season exceeds 8.5%, she can raise the advertising rates by 50% for the next season.
The population of viewer shares is normally distributed. A sample of the past 19 episodes
results in a mean share of 9.6% with a standard deviation of 10.0%. If Mak is willing to make
a Type 1 error with a 5% probability, which of the following statements is most accurate?

A)
B)
C)

Mak cannot charge a higher rate next season for advertising spots based on this
sample.
The null hypothesis Mak needs to test is that the mean share of viewers is
greater than 8.5%.
With an unknown population variance and a small sample size, Mak cannot test
a hypothesis based on her sample data.

Explanation
Mak cannot conclude with 95% confidence that the average share of viewers for the show
this season exceeds 8.5 and thus she cannot charge a higher advertising rate next season.
Hypothesis testing process:

Step 1: State the hypothesis. Null hypothesis: mean ≤ 8.5%; Alternative hypothesis: mean >
8.5%
Step 2: Select the appropriate test statistic. Use a t statistic because we have a normally
distributed population with an unknown variance (we are given only the sample variance)
and a small sample size (less than 30). If the population were not normally distributed, no
test would be available to use with a small sample size.
Step 3: Specify the level of significance. The significance level is the probability of a Type I
error, or 0.05.
Step 4: State the decision rule. This is a one-tailed test. The critical value for this question
will be the t-statistic that corresponds to a significance level of 0.05 and n-1 or 18 degrees
of freedom. Using the t-table, we determine that we will reject the null hypothesis if the
calculated test statistic is greater than the critical value of 1.734.
Step 5: Calculate the sample (test) statistic. The test statistic = t = (9.6 – 8.5) / (10.0 / √19) =
0.4795. (Note: Remember to use standard error in the denominator because we are
testing a hypothesis about the population mean based on the mean of 18 observations.)
Step 6: Make a decision. The calculated statistic is less than the critical value. Mak cannot
conclude with 95% confidence that the mean share of viewers exceeds 8.5% and thus she
cannot charge higher rates.
Note: By eliminating the two incorrect choices, you can select the correct response to this
question without performing the calculations.

(Module 6.2, LOS 6.g)

Question #27 of 86

Question ID: 1456615

In order to test whether the mean IQ of employees in an organization is greater than 100, a
sample of 30 employees is taken and the sample value of the computed test statistic, tn-1 =
3.4. The null and alternative hypotheses are:

A) H0: µ ≤ 100; Ha: µ > 100.
B) H0: X ≤ 100; Ha: X > 100.
C) H0: µ = 100; Ha: µ ≠ 100.
Explanation


The null hypothesis is that the population mean is less than or equal to from 100. The
alternative hypothesis is that the population mean is greater than 100.
(Module 6.1, LOS 6.b)

Question #28 of 86

Question ID: 1456634

Ron Jacobi, manager with the Toulee Department of Natural Resources, is responsible for
setting catch-and-release limits for Lake Norby, a large and popular fishing lake. He takes a
sample to determine whether the mean length of Northern Pike in the lake exceeds 18
inches. If the sample t-statistic indicates that the mean length of the fish is significantly
greater than 18 inches, when the population mean is actually 17.8 inches, the t-test resulted
in:

A) both a Type I and a Type II error.
B) a Type I error only.

C) a Type II error only.
Explanation
Rejection of a null hypothesis when it is actually true is a Type I error. Here, Ho: μ ≤ 18
inches and Ha: μ > 18 inches. Type II error is failing to reject a null hypothesis when it is
actually false.
Because a Type I error can only occur if the null hypothesis is true, and a Type II error can
only occur if the null hypothesis is false, it is logically impossible for a test to result in both
types of error at the same time.
(Module 6.1, LOS 6.c)

Question #29 of 86

Question ID: 1456625

A survey is taken to determine whether the average starting salaries of CFA charterholders is
equal to or greater than $59,000 per year. What is the test statistic given a sample of 135
newly acquired CFA charterholders with a mean starting salary of $64,000 and a standard
deviation of $5,500?

A) -10.56.
B) 0.91.
C) 10.56.


Explanation
With a large sample size (135) the z-statistic is used. The z-statistic is calculated by
subtracting the hypothesized parameter from the parameter that has been estimated and
dividing the difference by the standard error of the sample statistic. Here, the test statistic
= (sample mean – hypothesized mean) / (population standard deviation / (sample size)1/2)
= (X − µ) / (σ / n1/2) = (64,000 – 59,000) / (5,500 / 1351/2) = (5,000) / (5,500 / 11.62) = 10.56.

(Module 6.1, LOS 6.c)

Question #30 of 86

Question ID: 1456676

The variance of 100 daily stock returns for Stock A is 0.0078.  The variance of 90 daily stock
returns for Stock B is 0.0083.  Using a 5% level of significance, the critical value for this test is
1.61. The most appropriate conclusion regarding whether the variance of Stock A is different
from the variance of Stock B is that the:

A) variance of Stock B is significantly greater than the variance of Stock A.
B) variances are equal.
C) variances are not equal.
Explanation
A test of the equality of variances requires an F-statistic. The calculated F-statistic is
0.0083/0.0078 = 1.064. Since the calculated F value of 1.064 is less than the critical F value
of 1.61, we cannot reject the null hypothesis that the variances of the 2 stocks are equal.

(Module 6.4, LOS 6.j)

Question #31 of 86
Given the following hypothesis:
The null hypothesis is H0 : µ = 5
The alternative is H1 : µ ≠ 5
The mean of a sample of 17 is 7
The population standard deviation is 2.0
What is the calculated z-statistic?

Question ID: 1456650

A) 8.00.
B) 4.00.
C) 4.12.
Explanation
The z-statistic is calculated by subtracting the hypothesized parameter from the
parameter that has been estimated and dividing the difference by the standard error of
the sample statistic. Here, the test statistic = (sample mean − hypothesized mean) /
(population standard deviation / (sample size)1/2 = (X − μ) / (σ / n1/2) = (7 − 5) / (2 / 171/2) =
(2) / (2 / 4.1231) = 4.12.
(Module 6.2, LOS 6.g)

Question #32 of 86

Question ID: 1456628

Which of the following statements regarding hypothesis testing is least accurate?

A) A type I error is acceptance of a hypothesis that is actually false.
B) The significance level is the risk of making a type I error.
C) A type II error is the acceptance of a hypothesis that is actually false.
Explanation
A type I error is the rejection of a hypothesis that is actually true.
(Module 6.1, LOS 6.c)

Question #33 of 86

Question ID: 1456673

F-Table, Critical Values, 5 Percent in Upper Tail
Degrees of freedom for the numerator along top row
Degrees of freedom for the denominator along side row
10

12

15

20

24

30

25 2.24 2.16 2.09 2.01 1.96 1.92
30 2.16 2.09 2.01 1.93 1.89 1.84
40 2.08 2.00 1.92 1.84 1.79 1.74
Abby Ness is an analyst for a firm that specializes in evaluating firms involved in mineral
extraction. Ness believes that the earnings of copper extracting firms are more volatile than
those of bauxite extraction firms. In order to test this, Ness examines the volatility of returns
for 31 copper firms and 25 bauxite firms. The standard deviation of earnings for copper
firms was $2.69, while the standard deviation of earnings for bauxite firms was $2.92. Ness's
Null Hypothesis is σ12 = σ22. Based on the samples, can we reject the null hypothesis at a
90% confidence level using an F-statistic? Null is:

A) rejected. The F-value exceeds the critical value by 0.71.
B) not rejected.
C) rejected. The F-value exceeds the critical value by 0.849.

Explanation

F = s12 / s22 = $2.922 / $2.692 = 1.18
From an F table, the critical value with numerator df = 24 and denominator df = 30 is 1.89.
We cannot reject the null hypothesis.
(Module 6.4, LOS 6.j)

Question #34 of 86

Question ID: 1456610

Which one of the following is the most appropriate set of hypotheses to use when a
researcher is trying to demonstrate that a return is greater than the risk-free rate? The null
hypothesis is framed as a:

A)

greater than statement and the alternative hypothesis is framed as a less than
or equal to statement.


B)
C)

less than or equal to statement and the alternative hypothesis is framed as a
greater than statement.
less than statement and the alternative hypothesis is framed as a greater than
or equal to statement.

Explanation

If a researcher is trying to show that a return is greater than the risk-free rate then this
should be the alternative hypothesis. The null hypothesis would then take the form of a
less than or equal to statement.
(Module 6.1, LOS 6.b)

Question #35 of 86

Question ID: 1456640

The power of the test is:

A) the probability of rejecting a false null hypothesis.
B) equal to the level of confidence.
C) the probability of rejecting a true null hypothesis.
Explanation
This is the definition of the power of the test: the probability of correctly rejecting the null
hypothesis (rejecting the null hypothesis when it is false).
(Module 6.1, LOS 6.c)

Question #36 of 86
A Type I error is made when the researcher:

A) rejects the null hypothesis when it is actually true.
B) rejects the alternative hypothesis when it is actually true.
C) fails to reject the null hypothesis when it is actually false.
Explanation

Question ID: 1456626

A Type I error is defined as rejecting the null hypothesis when it is actually true. It can be
thought of as a false positive.
A Type II error occurs when a researching fails to reject the null hypothesis when it is false.
It can be thought of as a false negative.
(Module 6.1, LOS 6.c)

Question #37 of 86

Question ID: 1456632

Which of the following statements about hypothesis testing is most accurate? A Type I error
is the probability of:

A) rejecting a true null hypothesis.
B) rejecting a true alternative hypothesis.
C) failing to reject a false hypothesis.
Explanation
The Type I error is the error of rejecting the null hypothesis when, in fact, the null is true.
(Module 6.1, LOS 6.c)

Question #38 of 86

Question ID: 1456621

If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the
null is true, it is most likely that the:

A) probability of a Type I error is 2.5%.
B) power of the test is 95%.
C) significance level of the test is 5%.

Explanation
Rejecting the null hypothesis when it is true is a Type I error. The probability of a Type I
error is the significance level of the test. The power of a test is one minus the probability
of a Type II error, which cannot be calculated from the information given.
(Module 6.1, LOS 6.c)

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#39 f 86


Question #39 of 86

Question ID: 1456620

Which of the following statements about hypothesis testing is most accurate? A Type II error
is the probability of:

A) failing to reject a false null hypothesis.
B) rejecting a true alternative hypothesis.
C) rejecting a true null hypothesis.
Explanation
The Type II error is the error of failing to reject a null hypothesis that is not true.
(Module 6.1, LOS 6.c)

Question #40 of 86

Question ID: 1456612

Brian Ci believes that the average return on equity in the airline industry, µ, is less than 5%.
What are the appropriate null (H0) and alternative (Ha) hypotheses to test this belief?

A) H0: µ < 0.05 versus Ha: µ > 0.05.
B) H0: µ < 0.05 versus Ha: µ ≥ 0.05.
C) H0: µ ≥ 0.05 versus Ha: µ < 0.05.
Explanation
The null must be either equal to, less than or equal to, or greater than or equal to.

(Module 6.1, LOS 6.b)

Question #41 of 86

Question ID: 1456616

Susan Bellows is comparing the return on equity for two industries. She is convinced that
the return on equity for the discount retail industry (DR) is greater than that of the luxury
retail (LR) industry. What are the hypotheses for a test of her comparison of return on
equity?

A) H0: µDR > µLR versus Ha: µDR ≤ µLR.


B) H0: µDR ≤ µLR versus Ha: µDR > µLR.
C) H0: µDR < µLR versus Ha: µDR ≥ µLR.
Explanation
The alternative hypothesis is determined by the theory or the belief. It is essentially what
the analyst is trying to support, in this case that Ha: µDR > µLR
The opposite of the alternative will be the null hypothesis, in this case H0: µDR ≤ µLR

Remember that the null hypothesis can only have one of the following signs: ≥, ≤, =.
The alternative hypothesis, on the other hand, can only have one of these signs: <, >, ≠.
(Module 6.1, LOS 6.b)

Question #42 of 86

Question ID: 1456630

John Jenkins, CFA, is performing a study on the behavior of the mean P/E ratio for a sample
of small-cap companies. Which of the following statements is most accurate?

A)
B)
C)

A Type I error represents the failure to reject the null hypothesis when it is, in
fact, false.
One minus the confidence level of the test represents the probability of making
a Type II error.
The significance level of the test represents the probability of making a Type I
error.

Explanation
A Type I error is the rejection of the null when the null is actually true. The significance
level of the test (alpha) (which is one minus the confidence level) is the probability of
making a Type I error. A Type II error is the failure to reject the null when it is actually
false.

(Module 6.1, LOS 6.c)

Question #43 of 86

Question ID: 1456658


Student's t-Distribution
Level of Significance for One-Tailed Test
df 0.100 0.050 0.025 0.01 0.005 0.0005
Level of Significance for Two-Tailed Test
df

0.20

0.10

0.05

0.02

0.01

0.001

18 1.330 1.734 2.101 2.552 2.878

3.922

19 1.328 1.729 2.093 2.539 2.861

3.883

20 1.325 1.725 2.086 2.528 2.845

3.850

21 1.323 1.721 2.080 2.518 2.831

3.819

In a test of whether a population mean is equal to zero, a researcher calculates a t-statistic
of –2.090 based on a sample of 20 observations. If you choose a 5% significance level, you
should:

A) fail to reject the null hypothesis that the population mean is equal to zero.
B)
C)

reject the null hypothesis and conclude that the population mean is not
significantly different from zero.
reject the null hypothesis and conclude that the population mean is significantly
different from zero.

Explanation
At a 5% significance level, the critical t-statistic using the Student's t distribution table for a
two-tailed test and 19 degrees of freedom (sample size of 20 less 1) is ± 2.093. Because the
critical t-statistic of -2.093 is to the left of the calculated t-statistic of –2.090, meaning that
the calculated t-statistic is not in the rejection range, we fail to reject the null hypothesis
that the population mean is not significantly different from zero.

(Module 6.2, LOS 6.g)

Question #44 of 86

Question ID: 1456652


Student's t-Distribution
Level of Significance for One-Tailed Test
df 0.100 0.050 0.025 0.01 0.005 0.0005
Level of Significance for Two-Tailed Test
df

0.20

0.10

0.05

0.02

0.01

0.001

28 1.313 1.701 2.048 2.467 2.763

3.674

29 1.311 1.699 2.045 2.462 2.756

3.659

30 1.310 1.697 2.042 2.457 2.750

3.646

In order to test if the mean IQ of employees in an organization is greater than 100, a sample
of 30 employees is taken and the sample value of the computed test statistic, tn-1 = 1.2. If
you choose a 5% significance level you should:

A)
B)
C)

reject the null hypothesis and conclude that the population mean is greater
than 100.
fail to reject the null hypothesis and conclude that the population mean is not
greater than 100.
fail to reject the null hypothesis and conclude that the population mean is
greater than 100.

Explanation
At a 5% significance level, the critical t-statistic using the Student's t distribution table for a
one-tailed test and 29 degrees of freedom (sample size of 30 less 1) is 1.699 (with a large
sample size the critical z-statistic of 1.645 may be used). Because the critical t-statistic is
greater than the calculated t-statistic, meaning that the calculated t-statistic is not in the
rejection range, we fail to reject the null hypothesis and we conclude that the population
mean is not significantly greater than 100.
(Module 6.2, LOS 6.g)

Question #45 of 86

Question ID: 1456609

Jill Woodall believes that the average return on equity in the retail industry, µ, is less than
15%. If Woodall wants to examine the data statistically, what are the appropriate null (H0)
and alternative (Ha) hypotheses for her study?

A) H0: µ ≥ 0.15 versus Ha: µ < 0.15.


B) H0: µ < 0.15 versus Ha: µ > 0.15.
C) H0: µ < 0.15 versus Ha: µ ≥ 0.15.
Explanation
The alternative hypothesis may be thought of as what the analyst is trying to establish with
statistical evidence, in this case that µ < 0.15.
The opposite of the alternative will be the null hypothesis, in this case that µ ≥ 0.15.
Remember that the null hypothesis always includes the "equal to" condition: ≥, ≤, =.
The alternative hypothesis can only have one of these signs: <, >, ≠.
(Module 6.1, LOS 6.b)

Question #46 of 86

Question ID: 1456660

Which of the following statements about test statistics is least accurate?

A)
B)
C)

In a test of the population mean, if the population variance is unknown, we
should use a t-distributed test statistic.
In the case of a test of the difference in means of two independent samples, we
use a t-distributed test statistic.
In a test of the population mean, if the population variance is unknown and the
sample is small, we should use a z-distributed test statistic.

Explanation
If the population sampled has a known variance, the z-test is the correct test to use. In
general, a t-test is used to test the mean of a population when the population is unknown.
Note that in special cases when the sample is extremely large, the z-test may be used in
place of the t-test, but the t-test is considered to be the test of choice when the population
variance is unknown. A t-test is also used to test the difference between two population
means while an F-test is used to compare differences between the variances of two
populations.
(Module 6.2, LOS 6.g)

Question #47 of 86

Question ID: 1456672